Sunday, January 11, 2009

Symmetrical Inversion

Inspired again by Bartok's Mikrokosmos, I've written a canon in inversion at the octave.

As I mentioned two days ago, Mikrokosmos contains a wealth of compositional ideas. Though not a canon, #29 (book one) Imitáció tükörképben (Imitation Reflected) uses a strict inversion which causes some interesting pitch material. At this point in the book, Bartok is still using five-finger positions. The strict inversion of the first five notes of E major (in the right hand) inverts to the last five (or the first five below the tonic) pitches of E phrygian in the left hand. See the notated examples for clarity.

(click on image to enlarge)

As you can see, using the tonic as the axis of inversion, a major scale will always invert to a phrygian.

For my example, I used the phrygian in the right hand which reflects as major in the left. This time, though I still kept it short and simple, I didn't limit myself to a five finger position. I did, however, contain it within an octave in each hand.

I kept to mostly consonances and approached and left dissonances by step. The result certainly isn't 18th century in style...

(Click on image to enlarge)

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